A short carrot can be sown now, and will get to a decent size by close of play!
We only sow in buckets during the year, to deter the fly, but it's worth popping a few in the ground now as by the time they show, most of the flies will have gone!
I'd say parsnips would possibly be very small, as they really do need a long season, but hey, why not? They're lovely even as tiddlers!